The synchronization of chaotic systems

Abstract Synchronization of chaos refers to a process wherein two (or many) chaotic systems (either equivalent or nonequivalent) adjust a given property of their motion to a common behavior due to a coupling or to a forcing (periodical or noisy). We review major ideas involved in the field of synchronization of chaotic systems, and present in detail several types of synchronization features: complete synchronization, lag synchronization, generalized synchronization, phase and imperfect phase synchronization. We also discuss problems connected with characterizing synchronized states in extended pattern forming systems. Finally, we point out the relevance of chaos synchronization, especially in physiology, nonlinear optics and fluid dynamics, and give a review of relevant experimental applications of these ideas and techniques.